As you can see, the major difference between the Punjabis and me is my Southwest Asian and African percentages.

Now, I know that a quarter of my ancestry is not South Asian. So let’s try to estimate the admixture percentages for that ancestry. Being three-quarters Punjabi (I think), let’s average my sister’s and my results and then subtract 3/4th of the average Punjabi results from them. Then, multiply by 4 and you get NSA1 in the table above, which is supposedly my non-South-Asian ancestor.

Since some of the percentages are negative, I set those to zero and rescaled all the others so that they summed to 100%. That is NSA2.

For NSA2, we get the same five populations but the Egyptians and Palestinians exchange places.

This shows roughly that my quarter ancestry is most likely from the Middle East region of Egypt, Arabia or the Levant.

Let’s look at it another way. If I know that I have Punjabi and Egyptian ancestry, I can use the average Punjabi and average Egyptian admixture percentages to calculate my percentage of both ancestries since that has to sum to 100%. So:

Zack = p * Punjabi + (1-p) * Egyptian

And we solve for p using least squares.

I got 81.3% Punjabi for myself and 75.8% for my sister. On average, that’s 78.5% Punjabi and 21.5% Egyptian, which is pretty close to our genealogical information.